I am hoping this is a relatively simple answer. Ive always been interested in ar, and I've been debating about tinkering with a possibly ar driven ui for mobile.
I guess the only real question would be having the camera continuously turned on, how much battery would that use? i.e. would it be too much for something like this to be worth doing?
Battery drain is one of the biggest issues in the smartphones nowadays. I'm not a specialist in power consumption or battery life or whatever but anyone having and using a smartphone (not only for calls of course) would not be wrong by saying this. There are many tips on the internet teaching you how to increase the battery life. In fact processes running on your device need energy and that energy is provided by the battery.
To answer your question, I've been using the smartphones' cameras for AR applications since quite long time now. It's a heavy process and indeed it drains the battery faster than other processes. On the other hand you also have to consider the other processes running on your device while your AR application is used. For example your app might use the device's sensors (gyroscope, GPS, etc); these processes are draining the battery also. A simple test that you might do is to charge your device, start the camera and leave it until the battery dies. Well that's exactly how much the camera would drain the battery (you can even measure the time). Of course you might want to turn off everything else running on the device.
To answer your second question, it depends how the application is created (many things can be optimized a lot!) and how it's going to be used. If the goal of the application is to be used continuously for hours and hours then you need to wait for some other kind of technology being discovered (joking..I hope) or having extra power supply attached to your device. I think it's worth doing the application and optimize it on the fly and also in the end when everything is up an running. If the camera is the only issue then I'm sure it's worth trying!